The simple answer
to this is..... it doesn't. This date originates from one of the early church writers,
Hippolytus. It was also recorded in some of the early Roman documents as a celebratory
day of Pagan rituals. Christians not wanting to have anything to do with these rituals
made it a day of celebration of Jesus Christ.

The reality is we really don't know the exact date Christ was born. Some argue
that it couldn't be in the winter because to was too cold to care for flocks that
were in the field, but there are several instances of people tending to their flocks
at this time of the year, so that argument can not be made. As stated above, we just
don’t know the exact date.